Physics - Elasticity Question with Solution | TestHub

Strain energy per unit volume$u=\frac{U}{V}=\frac{1}{2}\times \mathrm{s}\mathrm{t}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\times \mathrm{s}\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{i}\mathrm{n}$

$\frac{U}{V}=\frac{1}{2}\times \frac{F}{A}\times \frac{∆l}{l}$

$\frac{U}{V}=\frac{1}{2}$$\text{Stress}\times \frac{\text{Stress}}{Y}$

$\therefore \frac{u_S}{u_L}=\frac{Y_L}{Y_S}\times {\left(\frac{\mathrm{Strain}\left(S\right)}{\text{Stress}\left(S\right)}\right)}^2={\left(\frac{A_L}{A_S}\right)}^2$

$={\left(\frac{r_L^2}{r_S^2}\right)}^2=\left(\frac{81}{1}\right)$